English

Computing endomorphism rings of elliptic curves under the GRH

Number Theory 2013-02-19 v2 Algebraic Geometry

Abstract

We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann hypothesis. Additionally, we improve the asymptotic complexity of previously known, heuristic, subexponential methods by describing a faster isogeny-computing routine.

Keywords

Cite

@article{arxiv.1101.4323,
  title  = {Computing endomorphism rings of elliptic curves under the GRH},
  author = {Gaetan Bisson},
  journal= {arXiv preprint arXiv:1101.4323},
  year   = {2013}
}

Comments

11 pages, 1 figure

R2 v1 2026-06-21T17:15:27.537Z